39 citations · 57 across the 22 of their papers we have counts for
23 papers
Transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by space-time white noise
Shijie Shang, Tusheng Zhang
In this paper, we establish transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by multiplicative space-time white noise. In p…
Ergodicity of reflected stochastic reaction-diffusion equations driven by space-time white noise
Shijie Shang, Jianliang Zhai, Tusheng Zhang
We consider the reflected stochastic reaction-diffusion equation on : \begin{align*} \left\{ \begin{aligned} d u(t,x) &=\frac{1}{2}\partial_{xx} u(t,x)dt +b(u(t,x))dt + σ(u(…
Ergodicity of stochastic reaction-diffusion equations on unbounded domains driven by space-time white noise
Shijie Shang, Jianliang Zhai, Tusheng Zhang
We consider the stochastic reaction-diffusion equation on the whole space: \begin{align*} \left\{ \begin{aligned} du(t,x) &=\frac{1}{2}\partial_{xx} u(t,x) dt+b(u(t,x))dt+ σ(u(t,x)…
Stochastic curve shortening flow driven by a transport-type pure jump Lévy noise
Xiaotian Ge, Shijie Shang, Weina Wu +1
We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump Lévy…
-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
Shijie Shang, Pengyu Wang, Tusheng Zhang
Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t…
Ergodicity of Stochastic two-phase Stefan problem driven by pure jump Lévy noise
Xiaotian Ge, Shijie Shang, Jianliang Zhai +1
In this paper, we consider stochastic two-phase Stefan problem driven by general jump Lévy noise. We first obtain the existence and uniqueness of the strong solution and then estab…
Large deviation principle for stochastic reaction-diffusion equations with super-linear drift on driven by space-time white noise
Yue Li, Shijie Shang, Jianliang Zhai
In this paper, we consider stochastic reaction-diffusion equations with super-linear drift on the real line driven by space-time white noise. A Freidlin-Wentzell large…
Transportation cost inequalities for stochastic reaction diffusion equations on the whole line
Yue Li, Shijie Shang, Tusheng Zhang
In this paper, we established quadratic transportation cost inequalities for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise on…
Hard Lefschetz theorems for free line bundles
Jiajun Hu, Shijie Shang, Jian Xiao
We introduce a partial positivity notion for algebraic maps via the defect of semismallness. This positivity notion is modeled on -positivity in the analytic setting and -amp…
Large deviations of fully local monotone stochastic partial differential equations driven by gradient-dependent noise
Tianyi Pan, Shijie Shang, Jianliang Zhai +1
Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple $$ \left\{ \begin{align} &dX_t=A(t…
Large deviations of stochastic heat equations with logarithmic nonlinearity
Tianyi Pan, Shijie Shang, Tusheng Zhang
In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by Brownian motion, which is neither…
Well-posedness of stochastic partial differential equations with fully local monotone coefficients
Michael Röckner, Shijie Shang, Tusheng Zhang
Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple : \begin{align*} \left\{ \begin{al…
A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves
Shijie Shang
We show that a bound of the Castelnuovo-Mumford regularity of any power of the ideal sheaf of a smooth projective complex variety is sharp exactly for comp…
Global well-posedness to stochastic reaction-diffusion equations on the real line with superlinear drifts driven by multiplicative space-time white noise
Shijie Shang, Tusheng Zhang
Consider the stochastic reaction-diffusion equation with logarithmic nonlinearity driven by space-time white noise: \begin{align}\label{1.a} \left\{ \begin{aligned} & \mathrm{d}u(t…
Stability of syzygy bundles on smooth projective varieties
Shijie Shang
We prove that the kernel bundle of the evaluation morphism of global sections, namely the syzygy bundle, of a sufficiently ample line bundle on a smooth projective variety is slope…
Stability of special generalized null correlation bundles on
Shijie Shang
In this paper, we study special generalized null correlation bundles on . We prove that special generalized null correlation bundles on are stable…
Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise
Shijie shang, Ran Wang
In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of solution to a stochastic heat equation defin…
Stochastic heat equations with logarithmic nonlinearity
Shijie Shang, Tusheng Zhang
In this paper, we establish the existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by Brownian motion on a bounded domain i…
Quadratic Transportation Cost Inequalities Under Uniform Distance For Stochastic Reaction Diffusion Equations Driven by Multiplicative Space-Time White Noise
Shijie Shang, Tusheng Zhang
In this paper, we established a quadratic transportation cost inequality for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise ba…
Approximations of Stochastic Navier-Stokes Equations
Shijie Shang, Tusheng Zhang
In this paper we show that solutions of two-dimensional stochastic Navier-Stokes equations driven by Brownian motion can be approximated by stochastic Navier-Stokes equations force…
Anticipating stochastic equation of two-dimensional second grade fluids
Shijie Shang
In this paper, we consider a stochastic model of incompressible second grade fluids on a bounded domain of R^2 driven by linear multiplicative Brownian noise with anticipating init…
Random dynamics of two-dimensional stochastic second grade fluids
Shijie Shang
In this paper, we consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of with multiplicative noise. We first show…
Strong solutions for a stochastic model of 2-D second grade fluids driven by Lévy noise
Shijie Shang, Jianliang Zhai, Tusheng Zhang
We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of driven by Lévy noise. Applying the variational approach,…